A12 scale
A12 (Playⓘ) is a non-octave-repeating scale or musical tuning featuring twelve steps to the tritave. As twelve steps to the octave is based on a triad of harmonics 4:5:6 (root, major third, perfect fifth), Playⓘ A12 is based on a triad of harmonics 4:7:10 (root, harmonic seventh, and compound major third).[1] Discovered by Heinz Bohlen between 1972 and 1973,[2] it was named "A12" by Enrique Moreno.[3] Bohlen considered this scale less logically consistent than the Bohlen–Pierce scale, which has thirteen steps in the twelfth.
Step | Ratio | Audio | Cents (just) | Audio | Cents (ET) | Difference |
---|---|---|---|---|---|---|
0 | 1/1 | Playⓘ | 0 | Playⓘ | 0 | 0 |
1 | 11/10 | Playⓘ | 165.00 | Playⓘ | 158.50 | -6.50 |
2 | 6/5 | Playⓘ | 315.64 | Playⓘ | 316.99 | 1.35 |
3 | 30/23 | Playⓘ | 459.99 | Playⓘ | 475.49 | 15.50 |
4 | 10/7 | Playⓘ | 617.49 | Playⓘ | 633.99 | 16.50 |
5 | 11/7 | Playⓘ | 782.49 | Playⓘ | 792.48 | 9.99 |
6 | 7/4 | Playⓘ | 968.83 | Playⓘ | 950.98 | -17.85 |
7 | 21/11 | Playⓘ | 1119.46 | Playⓘ | 1109.48 | -9.99 |
8 | 21/10 | Playⓘ | 1284.47 | Playⓘ | 1267.97 | -16.50 |
9 | 23/10 | Playⓘ | 1441.96 | Playⓘ | 1426.47 | -15.49 |
10 | 5/2 | Playⓘ | 1586.31 | Playⓘ | 1584.97 | -1.35 |
11 | 11/4 | Playⓘ | 1751.32 | Playⓘ | 1743.46 | -7.86 |
12 | 3/1 | Playⓘ | 1901.96 | Playⓘ | 1901.96 | 0 |
See also
- 833 cents scale
- Bohlen–Pierce scale
References
- ^ "Other Unusual Scales". The Bohlen–Pierce Site. Retrieved 27 November 2012.
- ^ Bohlen, Heinz: 13 Tonstufen in der Duodezime. Acustica, vol. 39 no. 2, S. Hirzel Verlag, Stuttgart, 1978, pp. 76 - 86. Cited in "Other Unusual Scales", The Bohlen–Pierce Site.
- ^ Moreno, Enrique Ignacio (Dec 1995). "Embedding Equal Pitch Spaces and The Question of Expanded Chromas: An Experimental Approach". Dissertation. Stanford University: 12–22. Cited in "Other Unusual Scales", The Bohlen–Pierce Site.
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Equal | |
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Linear | |
Irregular |
non-Western
- 833 cents scale
- A12 scale
- Alpha scale
- Beta scale
- Gamma scale
- Delta scale
- Lambda scale (Bohlen–Pierce)
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